Digital subscriber line (DSL) technologies can provide large bandwidth for digital communications over existing subscriber lines. When transmitting data over the subscriber lines, crosstalk interference can occur between the transmitted signals over adjacent twisted-pair phone lines, for example in a same or nearby bundle of lines. Crosstalk limits the performance of some DSL technologies, such as very high bit rate DSL 2 (VDSL2). The crosstalk in the subscriber lines can be eliminated or reduced using a crosstalk precoder, such as in a modem. The precoder may be used to modify and transmit signals from an exchange site downstream to a plurality of customer premise equipments (CPEs). The signals may be pre-distorted in a determined manner such that the pre-distortion in the signals and the crosstalk in the lines cancel out. Consequently, non-distorted signals that are substantially free of crosstalk may be received at the other end.
The precoder is trained or initialized using feedback signals from the CPEs, which may indicate the errors in the received signals at the CPEs. A sequence of pilot symbols are transmitted downstream to a VDSL transceiver remote unit (VTU-R) at the CPE, which returns corresponding error feedback signals to a VDSL transceiver office unit (VTU-O) at the exchange. The error feedback signals are used to train the precoder to adjust the pre-distorted signals until reaching convergence. The error feedback signals are provided from the CPEs to the exchange via a back channel and typically require a substantial data rate, e.g. for a plurality of subscriber lines. If the data rate cannot be met by the network standards, the feedback is provided to the precoder at a lower rate, such as using a subset of the tones in the pilot symbols in the subscriber lines. Using a subset of the tones to transmit a feedback signal may increase the initialization time of the precoder, lead to slower convergence of the precoder output, and reduce performance.
In some systems, to reduce the initialization time of the precoder, a sampling of the error feedback signals may be provided, e.g. using fewer frequencies in the error's frequency range. For example, the error feedback signal from a CPE may correspond to every n-th sub-carrier signal from a plurality of N sub-carriers, where N is the quantity of sub-carriers. The remaining portion of the signal, e.g. corresponding to the remaining frequencies or sub-carriers, may be interpolated from the received sampled feedback signal. However, using a sample of the error feedback signal to obtain a complete error feedback signal may reduce accuracy and performance. In other systems, the error feedback may be represented using fewer quantization bits, which may lead to slower error convergence and reduce performance.